Chief Executive Blair Jenkins was joined by other members of the Yes Scotland team, volunteers and The Proclaimers as he made the announcement in Edinburgh.
He said: "We are hugely grateful - not just to the one million plus people in Scotland who have now signed the Yes Declaration, but also to our many thousands of volunteers all around the country who have worked so hard to help us reach this target with just under a month still to go.
"More and more people are waking up to the fantastic opportunities created by a Yes vote. People realise that only with a Yes can we protect our NHS and other public services, grow our economy to create better jobs, and make Scotland a fairer society.
"Today's announcement is a clear indication of the level of support we're getting, and it gives us great confidence as we work towards securing a Yes majority on September 18."
The Yes Declaration and the one million target was announced by First Minister Alex Salmond on May 25, 2012, when the Yes campaign was officially launched.
The precise number of signatories at 4pm on Thursday, August 21, was 1,001,186.
Charlie Reid of the Proclaimers said: "With this fantastic target now hit, it looks like the Yes campaign is on its way to success. I certainly hope so. Nobody doubts that Scotland has the wealth, the talent and the ambition to be a successful independent country and we can make this a reality if only we grab this tremendous opportunity on September 18."
Craig Reid added: "We have so much going for us in Scotland. All we need is a bit of self-belief and with our own future in our own hands we can build a much better and much fairer country. Let's not let this fantastic opportunity slip from our grasp."
More than four million people are eligible to vote on September 18, and the predicted turnout is 75-80%, suggesting that around three million votes will be cast.